document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=53287>Question 53287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function? \r<BR>\n" );
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document.write( "Include the following in your answer: \r<BR>\n" );
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document.write( "Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence? <BR>\n" );
document.write( "Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric sequence? <BR>\n" );
document.write( "Give at least two real-life examples of a sequences or series. One example should be arithmetic, and the second should be geometric. Explain how these examples would affect you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #35545 by </B><A HREF=/tutors/aboutme.mpl?userid=Nate><B>Nate(3500)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Nate><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=35545\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Arithmetic Sequence can look like this: 0,2,4,6,8,10....x + 2<BR>\n" );
document.write( "Simply, you add two each time. Relatively, you just add a basic constant.<BR>\n" );
document.write( "This can be seen in a linear line as: y = 2x + 0<BR>\n" );
document.write( "A linear line shows that after <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > values there are the constant times that value for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Geometric Sequence can look like this: 1,3,9,27,81,243....3^x<BR>\n" );
document.write( "Simply, you just multiply by three eacch time.<BR>\n" );
document.write( "Think about this:<BR>\n" );
document.write( "for 0 values ~> 3^0 = 1<BR>\n" );
document.write( "for 1 value ~> 3^1 = 3<BR>\n" );
document.write( "for 2 values ~> 3*3 = 9<BR>\n" );
document.write( "Of course, this looks like: y = 3^x<BR>\n" );
document.write( "Geometric sequence looks like an exponential function.<BR>\n" );
document.write( "Example:<BR>\n" );
document.write( "Arithmetic: If you develop two bumps a day, how many bumps would you have in a week?! Explains that you should check a docter....<BR>\n" );
document.write( "Geometric: Bouncing of a ball may be decided as 1/3 of the previous bounce. This could better help you understand physics. Will the ball bounce forever? Mathematically, yes! Realistically, no! </SPAN>\n" );
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